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Abstract

We report on the development of a technique for differentiating between biological micro-objects using a rigorous, full-wave model of OCT image formation. We model an existing experimental prototype which uses OCT to interrogate a microfluidic chip containing the blood cells. A full-wave model is required since the technique uses light back-scattered by a scattering substrate, rather than by the cells directly. The light back-scattered by the substrate is perturbed upon propagation through the cells, which flow between the substrate and imaging system’s objective lens. We present the key elements of the 3D, Maxwell equation-based computational model, the key findings of the computational study and a comparison with experimental results.

Figures (16)

Schematic diagram of the image formation model composed of an OCT system and a microfluidic chip; a) a photo of the microfluidic chip and b) its depth resolved structure; c) the scattering volume design (TiO2 scatterers are not displayed); and d) an example OCT image showing the signals of interest.

Renders of the RBC and WBC refractive index models; a) a plot of the erythrocyte model topology; b) a three-dimensional rendering of the modeled erythrocyte surface, and c) a 3D rendering of the leukocyte (neutrophil) model.

Rendering of the staircase approximation to the TiO2 (a) and WBC granule (c), the result of simulations used to calculate the required value of Δ for modelling the TiO2 scatterers (b) and verification (d) that the granules are well represented by the shape in (c) for n3 ranging between nc and 1.6.

Rendering of the magnitude of electric field scattered by the discretized approximation to the TiO2 spheres using the PSTD method (a), and that of an ideal TiO2 sphere using Mie theory (b) for a plane wave polarized in the x-direction and propagating the z-direction. The field is normalized by the magnitude of the incident plane wave.

Plots of the phase-based differential parameter Slope; a) a horizontal profile through the experimentally acquired RBC signal; the blue line indicates a linear fit; b) a profile through the WBC signal plus linear fit; (c-d) simulated RBC and WBC profiles with linear fits. The black frame on the phase gradient ROI shown in (a) indicates the values used to calculate the first or last sample in the plot on the left. The label ‘Phase mean’ in the plots refers to the mean, taken over a rectangular frame, of phase gradient calculated for different positions of the frame.

Plots of the magnitude of the x-component of electric field, |Ex|; the plots shown in (a-d) are plotted in x-z plane containing the optical axis; a) the 3D homogeneous geometry for water only; b) a plot of |Ex| for the case presented in (a); c) the scattering geometry for the empty microchannel; d) a plot of |Ex| for the case presented in (c); e) plots of |Ex| in x-y planes spaced about the beam’s focus: the top row of images shows the plots associated with (a-b), and the lower shows those associated with (c-d).

Magnitude plots of the x-component of electric field, |Ex|, for the cases of an RBC and WBC present in the microchannel; the plots shown in (a-d) are plotted in x-z plane containing the optical axis; a) the scattering geometry for the RBC included in the microchannel; b) a plot of |Ex| for the case (a); (c-d) the plots corresponding to (a-b) but with a WBC in the microchannel; e) plots of |Ex| in x-y planes: the top row of images for the RBC case (i.e., a-b), and the lower row corresponds to the WBC case (i.e., c-d).

a) Simulated magnitude M-scans constructed from 407 A-scans; b) the M-scan from (a) with static background subtracted (differential magnitude M-scan); c) phase gradient M-scan based on complex M-scan shown as magnitude in (a). The left signal of interest in all M-scans refers to the RBC, while the right one to the WBC.

Comparison of simulated and experimental M-scans for data set 1; a) a simulated magnitude M-scan; b) the M-scan from (a) with background subtracted; c) an experimental M-scan created by fusing two independent M-scans (the top image shows a part of M-scan including a signal coming from the WBC and the lower image shows a signal derived from the RBC); d) the M-scans from (c) with background subtracted; e) the simulated M-scan from (a) divided by its dynamic range and with white noise, of standard deviation taken from (g), added; f) the simulated M-scan from (b) processed in the same way as (e) with noise derived from (h); g) the experimental M-scan from (c), divided by its dynamic range; h) the experimental M-scan from (d) processed in the same way as (g).

Illustration of the attenuation of the OCT signal (magnitude); all plots and images are presented in decibel scale; a) profiles (A-scans) through the signals of interest for: experimental RBC (red line, depicted as an image in (e), data set 2), experimental WBC (black line, data set 2), simulated RBC (green line, also depicted in (f)) and simulated WBC (blue line). The dashed lines (magenta) indicate the SNR level for data set 2 (34dB); b) the corresponding profiles for data set 1 (SNR 38dB); (c-d) the profiles through the TiO2-PDMS layer in the absence of cells: experimental (orange lines, shown as the images in (g-h)), for experimental data set 2 (c) and data set 1 (d), and simulated profiles (brown lines) also depicted in (i). The vertical lines in images (e-f) indicate the origin of the associated profile plots.

Plots illustrating the sensitivity of the differential parameters to axial position of the ROI, calculated for simulated (the left column in each frame) and exemplar experimental data (the right columns), which consists of 130 RBC signals and 130 WBC signals, derived from experimental data set 2. The parameter values shown in row (b) in the left frame are presented in logarithmic scale. The red line in each plot indicates differential parameters obtained for the RBC signals, while the black line corresponds to the WBCs.

Metrics

Table 1

Parameters of the numerical simulation. Most of symbols are defined in Fig. 4; ΔλMAX stands for maximum spectral width (wavelength width) and NAOB2 indicates numerical aperture of the objective lens OB2.

Parameter

Value

λ0

790nm

ΔλMAX

250nm

NAOB2

0.11

fOB1

9mm

fOB2

18mm

f1

53.5mm

f2

75mm

Optical fiber

Single mode fiber Corning HI 780 (MFD = 5.5μm)

Table 2

Differential parameters.

Magnitude-based differential parameters

Phase-based differential parameters

No.

Differential parameter

No.

Differential parameter

1

Standard deviations (a.u.)

4

Standard deviations (rad)

2

Axial (vertical) speckle size (μm)

5

Phase 2DFT (Contrast Top-Middlea) (a.u.)

3

Speckle contrast (‒)

6

Slope (‒)

Tables (2)

Table 1

Parameters of the numerical simulation. Most of symbols are defined in Fig. 4; ΔλMAX stands for maximum spectral width (wavelength width) and NAOB2 indicates numerical aperture of the objective lens OB2.